---
title: "Gibbard-Satterthwaite Games"
authors:
  - "Edith Elkind"
  - "Umberto Grandi"
  - "Francesca Rossi"
  - "Arkadii M. Slinko"
doi: ""
url: "https://ijcai.org/proceedings/2015/81"
pdf: "https://ijcai.org/proceedings/2015/0081.pdf"
venue: "Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence"
year: 2015
pages: "533-538"
track: "Main Track"
keywords:
---

# Gibbard-Satterthwaite Games

Edith Elkind, Umberto Grandi, Francesca Rossi, Arkadii M. Slinko

*Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence*, pages 533-538.

## Abstract

The Gibbard-Satterthwaite theorem implies the ubiquity of manipulators — voters who could change the election outcome in their favor by unilaterally modifying their vote. In this paper, we ask what happens if a given profile admits several such voters. We model strategic interactions among Gibbard–Satterthwaite manipulators as a normal-form game. We classify the 2-by-2 games that can arise in this setting for two simple voting rules, namely Plurality and Borda, and study the complexity of determining whether a given manipulative vote weakly dominates truth-telling, as well as existence of Nash equilibria.